Dangerous Border-Collision bifurcations of a piecewise-smooth map

Hun Ki Baek; Younghae Do

doi:10.3934/cpaa.2006.5.493

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2006, Volume 5, Issue 3: 493-503. Doi: 10.3934/cpaa.2006.5.493

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Dangerous Border-Collision bifurcations of a piecewise-smooth map

Hun Ki Baek^1, and
Younghae Do^1,

1.
Department of Mathematics, Kyungpook National University, Daegu, 702-701

Received: May 31, 2005

Revised: January 31, 2006

Published: August 2006

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Abstract

In this paper we study the dangerous border-collision bifurcations [8] which recently have been numerically found on piecewise smooth maps characterized by non-differentiability on some surface in the phase space. The striking feature of such bifurcations is characterized by exhibiting a stable fixed point before and after the critical bifurcation point, but the unbounded behavior of orbits at the critical bifurcation point. We consider a specific variable space in order to do an analytical investigation of such bifurcations and prove the stability of fixed points. We also extend these bifurcation phenomena for the fixed points to the multiple coexisting attractors.

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Mathematics Subject Classification: 37C05, 37C37, 37G35, 37H20.

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